The Nineteenth Israeli Mini-Workshop in Applied and Computational Mathematics

David Fajman (University of Vienna)

Decay estimates for geometric transport equations

We introduce a Vector Field Method for transport equations inspired by the original technique of Klainerman, developed for nonlinear wave equations. Our method provides sharp decay estimates for the energy density of solutions to transport equations in various systems. We describe how the method can be applied to prove nonlinear stability results for systems of transport equations coupled to other types of evolutionary PDEs in nontrivial geometric backgrounds.

Joint work with J. Joudioux (Vienna) and J. Smulevici (Paris).

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